The standard answers...light-colored, smooth yarn and needles that feel comfortable in your hand. Some people start beginners on size 8s, some on 10s, but the final answer has to be "...depending on what you like, can get and can use." What kind of yarn is always an argument-starter, because some people will not use acrylic and some will not use wool. Your first yarn should be something that can put up with being ripped out repeatedly. Avoid anything horribly expensive or fuzzy.
I'd avoid making a big project for your first one. Try, maybe, a cell phone case, a pair of handwarmers or a dishcloth. Sugar n' Cream and Peaches n'Cream are a couple of sturdy, inexpensive cotton yarns that make great dishcloths, mug mats and the like. By inexpensive, I mean you can usually get a small skein for a buck-fifty US. I'm one of those who does like acrylic yarn, and yes, I will use Red Heart because with the way I happen to knit it wears well, but if you want instant gratification (who doesn't?) Lion BRand Jiffy will do nicely.
If you do a vest, pick a very simple pattern without too much shaping. You'll still need to know how to increase and decrease, but if you take your time and don't get upset if it isn't perfect right away, you'll be fine.
As for wool, if you don't have problems handling it, and you can find some at a decent price (Cascade 220 and Lion Wool both come to mind, but everyone has a favorite), you can try felting. It's great when you start because any mistakes you make are reeeeeally hard to see once you felt the project